A Physical Unclonable Function (PUF) is a hardware circuit which generates one or more codes according to physical random performances of hardware devices, and thus difficult if not impossible, to duplicate. PUFs are widely used in data security in the military and commercial applications, e.g., unmanned vehicles, cloud computing, etc. A PUF can be used in almost any application in which a random number is required. Such applications preferably require the codes to be random chip over chip such that even if an exact layout of the chip is reproduced by reverse engineering, the set of codes of the reproduced chip are different from the original chip. The set of values generated by one chip must be constant over time, voltage, temperature, etc.